This study addresses the question of how simple networks can account for a variety of phenomena associated with the shift of a specialized processing focus across the visual scene. We address in particular aspects of the dichotomy between the preattentive-paralel and the attentive-serial modes of visual perception and their hypothetical neuronal implementations. Specifically we propose the following: 1.) A number of elementary features, such as color, orientation, direction of movement, disparity ect. are represented in parallel in different topographical maps, called the early representation. 2.) There exists a selective mapping from this early representation into a more central representation, such that at any instant the central representation contains the properties of only a single location in the visual scene, the selected location. 3.) We discuss some selection rules that determine which location will be mapped into the central representation. The major rule, using the saliency or conspicuity of locations in the early representation, is implemented using a so-called Winner-Take-All network. A hierarchical pyramid-like architecture is proposed for this network. We suggest possible implementatinos in neuronal hardware, including a possible role for the extensive back-projection from the cortex to the LGN.